Quadratic Dissipation Effect on the Moonpool Resonance

This paper adopted a semi-analytical method based on eigenfunction matching to solve the problem of sharp resonance of cylindrical structures with a moonpool that has a restricted entrance. To eliminate the sharp resonance and to measure the viscous effect, a quadratic dissipation is introduced by assuming an additional dissipative disk at the moonpool entrance. The fluid domain is divided into five cylindrical subdomains, and the velocity potential in each subdomain is obtained by meeting the Laplace equation as well as the boundary conditions. The free-surface elevation at the center of the moonpool, along with the pressure and velocity at the restricted entrance for first-order wave are evaluated. By choosing appropriate dissipation coefficients, the free-surface elevation calculated at the center of the moonpool is in coincidence with the measurements in model tests both at the peak period and amplitude at resonance. It is shown that the sharp resonance in the potential flow theory can be eliminated and the viscous effect can be estimated with a simple method in some provided hydrodynamic models.     

Diffraction of Water Waves by A Vertically Floating Cylinder in A Two-Layer Fluid

In this paper, the diffraction of water waves by a vertically floating cylinder in a two-layer fluid of a finite depth is studied. Analytical expressions for the hydrodynamic loads on the vertically floating cylinder are obtained by use of the method of eigenfunction expansions. The hydrodynamic loads on the vertically floating cylinder in a two-layer fluid inelude not only the surge, heave and pitch exciting forces due to the incident wave of the surface-wave mode, but also those due to the incident wave of the internal-wave mode. This is different from the case of a homogenous fluid. Some given examples show that, for a two-layer fluid system with a small density difference, the hydrodynamic loads for the surface-wave mode do not differ significantly from those due to surface waves in a single-layer fluid, but the hydrodynamic loads for the internal-wave mode are important over a wide range of frequencies. Moreover, also considered are the free surface and interface elevations generated by the diffraction wave due to the incident wave of the surface-wave and interhal-wave modes, and transfer of energy between modes.     

Interaction of linear waves with an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth

The linear water wave scattering and radiation by an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth is investigated by use of the multipole expansion method. The diffracted and radiated potentials are expressed as a linear combination of infinite multipoles placed at the centre of each cylinder with unknown coefficients to be determined by the cylinder boundary conditions. Analytical expressions for wave forces, hydrodynamic coefficients, reflection and transmission coefficients and energies are derived. Comparisons are made between the present analytical results and those obtained by the boundary element method, and some examples are presented to illustrate the hydrodynamic behavior of multiple horizontal circular cylinders in a two-layer fluid. It is found that for two submerged circular cylinders the influence of the fluid density ratio on internal-mode wave forces is more appreciable than surface-mode wave forces, and the periodic oscillations of hydrodynamic results occur with the increase of the distance between two cylinders; for four submerged circular cylinders the influence of adding two cylinders on the wave forces of the former cylinders is small in low and high wave frequencies, but the influence is appreciable in intermediate wave frequencies.     

Second-order random interfacial wave solutions for two-layer fluid with a free surface

1 Introduction Interfacial waves travelling along the interface between two fluids of different densities can be often observed in subsurface layers of the ocean since the upper subsurface layer is warmer over much of the o- cean (Umeyama, 2002). They are…     

Green functions with pulsating sources in a two-layer fluid of finite depth

The derivation of Green function in a two-layer fluid model has been treated in different ways.In a two-layer fluid with the upper layer having a free surface,there exist two modes of waves propagating due to the free surface and the interface.This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating.The source point is located either in the upper or lower part of a two-layer fluid of finite depth.The derivation is carried out by the method of singularities.This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present.Furthermore,experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results.Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower,for each case.The effect of the density on the internal waves is demonstrated.Also,it is shown how the surface and internal wave amplitudes are compared for both the wave modes.The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.     

Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a two-layer fluid system

Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer .uid with a top free surface and a .at bottom. The solutions were deduced from the general form of linear .uid dynamic equations of two-layer .uid under the f -plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. (2004. Science in China, Ser. D, 47(12): 1147–1154) for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the in.uence of the earth’s rotation both on the surface wave solutions and the interfacial wave solutions should be considered.     

Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a twolayer fluid system

Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a flat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. (2004. Science in China, Ser. D, 47(12):1147-1154) for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth''s rotation both on the surface wave solutions and the interfacial wave solutions should be considered.     

On natural frequencies and modal shapes in two-dimensional asymmetric and symmetric moonpools in finite water depth

In this paper theoretical models are proposed for computing the natural frequencies and modal shapes of two-dimensional asymmetric and symmetric moonpools in the finite water depth. The boundary value problem is solved by using a domain decomposition approach. On the outer vertical boundary bounded by the beam of the two bodies, linearized velocity potential is assumed to be nil. Eigenvalue problem is formulated by matching the velocity potential and fluid flux on the common boundaries to obtain the natural frequencies and modal shapes of the free surface elevation. In the symmetric moonpool cases, so-called single mode approximations (SMA) have been derived and can be adopted for rapid estimation of the natural frequencies for both piston and sloshing modes. The present results have been extensively compared with the solutions using the two-dimensional infinite water depth model developed by Molin [1], the numerical solutions and experimental data by Faltinsen et al. [2]. It is found that the solutions have been improved from the infinite water depth model. It is demonstrated that the proposed models can well predict the resonance frequencies and modal shapes for the two-dimensional asymmetric and symmetric moonpools.     

水下平板与波浪相互作用完全非线性数值模拟(英文)

利用完全非线性数值波浪水槽技术研究水下平板与波浪的相互作用。假定水下平板厚度极薄、刚性,位于有限水深并且非常接近自由水面。应用四阶龙格库塔方法追踪每一时刻的波面形状,采用阻尼层来吸收反射波以保证算法的稳定性,同时引入平滑和重组的方法抑制自由表面控制点的较高梯度。通过对波浪与浮动圆柱相互作用的数值模拟证实了数值波浪水槽方法的有效性,计算结果与线性理论吻合良好。在波浪数值水槽方法中引入造波板模拟波浪产生并与水下平板发生相互作用,应用傅立叶解析方法对波面变形、波浪力作了分析。结果表明在板非常接近自由水面的情况下会表现出现很强的非线性,揭示了线性理论的局限性。     

Coupling Response of Heave and Moonpool Water Motion of A Truss Spar Platform in Random Waves

This paper presents the heave responses and the moonpool water motions of a truss Spar platform with semi-closed moonpool in random waves. A 2-DOF(degree of freedom) coupling dynamical equations of the platform heave and vertical motions of the moonpool water are derived. The linear wave theory is used to simulate the random waves. The response statistical values and the power spectrums are calculated to analyze the mutual influences between the platform heave and the moonpool water motions for different opening ratios of the moonpool. The effect of coupling parameters on the platform heave and the moonpool water motions are analyzed. The results show that motions of the moonpool water significantly affected the platform heave when the characteristic wave period is far away from the natural period of the platform heave, and different moonpool opening ratios lead to different heave amplitudes of the platform. In the actual design, an optimized moonpool opening ratio can be designed to reduce heave motions of the platform.     

Waves at the sea surface generated by a flow over an underwater obstacle

We study wave perturbations appearing at the surface of a two-layer fluid flowing around an underwater obstacle in the lower layer of the fluid. The obstacle is modeled as a point source. A class of asymptotic solutions was obtained that demonstrate that realistic conditions of the open sea and the given parameters of the source in the neighborhood of the source of hydrodynamic perturbations allow for the formation of two types of surface waves. The waves of the first type only slightly depend on the stratification, and, in the conditions of the real sea, they are almost not observed. The characteristics of the second type of waves were repeatedly recorded in field experiments during radar and optical monitoring of the sea surface.     

The effect of appendages on the hydrodynamic characteristics of an underwater vehicle near the free surface

An underwater vehicle typically has various appendages such as sail, rudders and hydroplanes. These appendages affect the hull hydrodynamic characteristics, including the resistance components and the form of the generated wave due to the motion of the vehicle near the free surface. The effect of the appendages on the hydrodynamic characteristics of an underwater vehicle near the free surface is studied. Initially the DARPPA SUBOFF submarine without the appendages is selected and hydrodynamic characteristics, including the friction resistance, viscous pressure resistance, wave resistance and shape of the created wave on the free surface are calculated for Froude numbers in the range of 0.128–0.84 and non-dimensional submergence depths 1.3, 2.2, 3.3 & 4.4. Then, by adding the appendages and comparing these two conditions, the effect of appendages is obtained. The results of computations indicate that the appendages cause a mean increase of about 16% in the total resistance. This increment is due to viscosity of fluid and also the interaction of the main hull with the appendages. There are no significant changes in the wave pattern and wave making resistance due to the presence of appendages.     

楔形体在波浪中自由入水的数值模拟

物体入水时波浪的影响不可忽略,基于流体力学模型采用VOF法,并利用自定义函数,模拟了楔形体的自由入水过程;同时结合推波板原理及海绵层消波理论实现了数值水槽的造消波,完成了波浪中楔形体自由入水的模拟,计算了楔形体入水时所受的水作用力、自由液面变化及物面压强分布等,研究了不同波高、周期以及在波浪不同位置入水时对楔形体的影响。结果表明:本文建立的数值模型可很好地模拟楔形体入水造成的射流及空泡的形成发展过程,波浪对楔形体入水的影响主要由波浪内部流场变化及表面波形决定,在波浪不同位置处入水对楔形体受力及入水形态均有较大影响。     

Laboratory modeling of the propagation of periodic internal waves over bottom slopes

The experimental investigation of the run-up of periodic internal waves in a two-layer fluid on the coastal slope is performed in an open hydrochannel at the Physical Department of the Lomonosov Moscow State University. The waves are produced by a wave generator. We study the transformation of waves, the vertical structure of the field of velocities of mass transfer, and the behavior of the parameters of internal waves propagating over the sloping bottom. It is shown that the run-up and breaking of internal waves are accompanied by periodic emissions of portions of the heavier fluid from the bottom layer upward along the slope. The Stokes drift velocity changes its sign as a function of depth. Moreover, both the wave length (the horizontal distance between the neighboring crests) and the height of waves over the sloping bottom (the elevation of the crest over the slope along the vertical) decrease as the wave approaches the coast.     

An experimental study of stratified mixing caused by internal solitary waves in a two-layered fluid system over variable seabed topography

Stratified mixing is observed in a wave flume on an internal solitary wave (ISW) of depression or elevation type propagating over a submarine ridge. The submarine ridges, which comprise the seabed topography, are either semicircular or triangular. Tests are performed in a series of combinations of submarine ridges with different heights and ISW in different amplitudes within a two-layer fluid system. When the thickness of the top layer is less than that of the lower layer (i.e., H₁<H₂), a depression-type ISW may produce a strong hydraulic jump with downwards motion and continuous eddy diffusion. During diffusion, the leading profile of the ISW transforms a wrapped vortex on the front face of the ridge, and a vortex separation at the apex of the ridge. Meanwhile, an elevation-type ISW causes a vortex in the lee of a submarine ridge, which resembles a surface solitary wave in terms of wave transmission process. The degree of wave-obstacle interaction is determined by energy loss, which is induced by submarine ridge blockage. The experiment results suggest that degree of blocking can be applied to classify various degrees of ISW-obstacle encounter in the stratified two-layer fluid system.     

Hydroelastic interaction between obliquely incident waves and a semi-infinite elastic plate on a two-layer fluid

The hydroelastic response of a semi-infinite thin elastic plate floating on a two-layer fluid of finite depth due to obliquely incident waves is investigated. The upper and lower fluids with different densities separated by a sharp and stable interface are assumed to be inviscid and incompressible and the motion to be irrotational. Simply time-harmonic incident waves of the surface and interfacial wave modes with a given angular frequency are considered within the framework of linear potential flow theory. With the aid of the methods of matched eigenfunction expansion and the inner product of the two-layer fluid, a closed system of simultaneous linear equations is derived for the reflection and transmission coefficients of the series solutions. Based on the dispersion relations for the gravity waves and the flexural–gravity waves in a two-layer fluid and Snell’s law for refraction, we obtain a critical angle for the incident waves of the surface wave mode and three critical angles for the incident waves of the interfacial wave mode, which are related to the existence of the propagating waves. Graphical representations of the series solutions show the interaction between the water waves and the plate. The effects of several physical parameters, including the density and depth ratios of the fluid and the thickness of the plate, on the wave scattering and the hydroelastic response of the plate are studied. It is found that the variation of the thickness of the plate may change the wave numbers and the critical angles. The density ratio is the main factor to influence the wave numbers of the interfacial wave modes. Finally, the stress state is considered.     

内孤立波中半潜平台动力响应特性

基于内孤立波mKdV理论,采用时域有限位移运动方程,结合改进的Morison公式,研究了两层流体中内孤立波与带分段式悬链系泊约束半潜平台的相互作用问题。针对东沙群岛南部海域附近某实测内孤立波特征参数,计算分析了在该内孤立波作用下SEDCO-700型半潜平台的内孤立波载荷、运动响应及其系泊张力的变化特性。研究表明,内孤立波不仅会对半潜平台产生突发性冲击载荷作用,使其产生大幅度水平漂移运动,并导致其系泊张力显著增大,因此在半潜平台等深海平台的设计与应用中,内孤立波的影响是不可忽视的。     

Nonlinear response of membranes to ocean waves using boundary and finite elements

The behavior of a highly deformable membrane to ocean waves was studied by coupling a nonlinear boundary element model of the fluid domain to a nonlinear finite element model of the membrane. The hydrodynamic loadings induced by water waves are computed assuming large body hydrodynamics and ideal fluid flow and then solving the transient diffraction/radiation problem. Either linear waves or finite amplitude waves can be assumed in the model and thus the nonlinear kinematic and dynamic free surface boundary conditions are solved iteratively. The nonlinear nature of the boundary condition requires a time domain solution. To implicitly include time in the governing field equation, Volterra's method was used. The approach is the same as the typical boundary element method for a fluid domain where the governing field equation is the starting point. The difference is that in Volterra's method the time derivative of the governing field equation becomes the starting point.The boundary element model was then coupled through an iterative process to a finite element model of membrane structures. The coupled model predicts the nonlinear interaction of nonlinear water waves with highly deformable bodies. To verify the coupled model a large scale test was conducted in the OH Hinsdale wave Research Laboratory at Oregon State University on a 3-ft-diameter fabric cylinder submerged in the wave tank. The model data verified the numerical prediction of the structure displacements and of the changes in the wave field.The boundary element model is an ideal modeling technique for modeling the fluid domain when the governing field equations is the Laplace equation. In this case the nonlinear boundary element model was coupled with a finite element model of membrane structures, but the model could have been coupled with other finite element models of more rigid structures, such as a pontoon floating breakwater.